Noether Currents and Maxwell-Type Equations of Motion in Higher Derivative Gravity Theories

In general coordinate invariant gravity theories whose Lagrangians contain arbitrarily high order derivative fields, the Noether currents for the global translation and for the Nakanishi’s IOSp(8|8) choral symmetry containing the BRS symmetry as its member are constructed. We generally show that for each of these Noether currents, a suitable linear combination of equations of motion can be brought into the form of a Maxwell-type field equation possessing the Noether current as its source term.

The Calculation of High-Order Vertical Derivative in Gravity Field by Tikhonov Regularization Iterative Method

In mathematics, statistics, and computer science, particularly in the fields of machine learning and inverse problems, regularization is a process of introducing additional information in order to solve an ill-posed problem or to prevent overfitting. The Tikhonov regularization method is widely used to solve complex problems in engineering. The vertical derivative of gravity can highlight the local anomalies and separate the horizontal superimposed abnormal bodies. The higher the order of the vertical derivative is, the stronger the resolution is. However, it is generally considered that the conversion of the high-order vertical derivative is unstable. In this paper, based on Tikhonov regularization for solving the high-order vertical derivatives of gravity field and combining with the iterative method for successive approximation, the Tikhonov regularization method for calculating the vertical high-order derivative in gravity field is proposed. The recurrence formula of Tikhonov regularization iterative method is obtained. Through the analysis of the filtering characteristics of this method, the high-order vertical derivative of gravity field calculated by this method is stable. Model tests and practical data processing also show that the method is of important theoretical significance and practical value.

High-order derivative fusion estimation of rotorcraft angular rate

Purpose The paper aims at developing a novel algorithm to estimate high-order derivatives of rotorcraft angular rates to break the contradiction between bandwidth and filtering performance because high-order derivatives of angular rates are crucial to rotorcraft control. Traditional causal estimation algorithms such as digital differential filtering or various tracking differentiators cannot balance phase-lead angle loss and high-frequency attenuation performance of the estimated differentials under the circumstance of strong vibration from the rotor system and the rather low update rate of angular rates. Design/methodology/approach The algorithm, capable of estimating angular rate derivatives to maximal second order, fuses multiple attitude signal sources through a first-proposed randomized angular motion maneuvering model independent of platform dynamics with observations generated by cascaded tracking differentiators. Findings The maneuvering flight test on 5-kg-level helicopter and the ferry flight test on 230-kg-level helicopter prove such algorithm is feasible to generate higher signal to noise ratio derivative estimation of angular rates than traditional differentiators in regular flight states with enough bandwidth for flight control. Research limitations/implications The decrease of update rate of input attitude signals will weaken the bandwidth performance of the algorithm and higher sampling rate setting is recommended. Practical implications Rotorcraft flight control researchers and engineers would benefit from the estimation method when implementing flight control laws requiring angular rate derivatives. Originality/value A purely kinematic randomized angular motion model for flight vehicle is first established, combining rigid-body Euler kinematics. Such fusion algorithm with observations generated by cascaded tracking differentiators to estimate angular rate derivatives is first proposed, realized and flight tested.

A New Derivative-Free Method to Solve Nonlinear Equations

A new high-order derivative-free method for the solution of a nonlinear equation is developed. The novelty is the use of Traub’s method as a first step. The order is proven and demonstrated. It is also shown that the method has much fewer divergent points and runs faster than an optimal eighth-order derivative-free method.

Local convergence of tensor methods

In this paper, we study local convergence of high-order Tensor Methods for solving convex optimization problems with composite objective. We justify local superlinear convergence under the assumption of uniform convexity of the smooth component, having Lipschitz-continuous high-order derivative. The convergence both in function value and in the norm of minimal subgradient is established. Global complexity bounds for the Composite Tensor Method in convex and uniformly convex cases are also discussed. Lastly, we show how local convergence of the methods can be globalized using the inexact proximal iterations.

A high order derivation method for distribution network transient data

Nowadays, high-order data needs to be processed quickly and accurately by various algorithms in distribution networks. It is difficult to ensure the accuracy of calculation both in low-order and high-order cases, due to the theoretical limitations of traditional high-order derivation methods. Aimed to improve the calculation accuracy, a new high-order derivative method based on the polynomial fitting is proposed in this paper. By analyzing the transient characteristics of voltage and current signals in the distribution network, the base fitting-function can be selected, and the coefficient of the base function can be obtained to fit the objective function by the least square method. The original discrete data will be replaced by new fitting-function for derivative operation, which not only ensures the anti-interference ability, but also overcomes the limitations of the traditional polynomial fitting method in high-order cases. The simulation results show that this method has high accuracy in high-order and low-order cases, and has good accuracy and anti-interference ability.

Detecting Inverse Boundaries by Weighted High-Order Gradient Collocation Method

The weighted reproducing kernel collocation method exhibits high accuracy and efficiency in solving inverse problems as compared with traditional mesh-based methods. Nevertheless, it is known that computing higher order reproducing kernel (RK) shape functions is generally an expensive process. Computational cost may dramatically increase, especially when dealing with strong-from equations where high-order derivative operators are required as compared to weak-form approaches for obtaining results with promising levels of accuracy. Under the framework of gradient approximation, the derivatives of reproducing kernel shape functions can be constructed synchronically, thereby alleviating the complexity in computation. In view of this, the present work first introduces the weighted high-order gradient reproducing kernel collocation method in the inverse analysis. The convergence of the method is examined through the weights imposed on the boundary conditions. Then, several configurations of multiply connected domains are provided to numerically investigate the stability and efficiency of the method. To reach the desired accuracy in detecting the outer boundary for two special cases, special treatments including allocation of points and use of ghost points are adopted as the solution strategy. From four benchmark examples, the efficacy of the method in detecting the unknown boundary is demonstrated.

Nonlinear differential and integral sliding mode control for wave compensation system of ship-borne manipulator

Ship-borne manipulator system is extremely unstable under the complex marine environment, which seriously threatens the safety of operating equipment and operators. In this paper, the dynamics and robust control of wave compensation system for ship-borne manipulator are studied. First, based on the oil circuit variable amplitude control of ship-borne manipulator, the coupling dynamic model of valve-controlled cylinder parallel accumulator is established. Then, since traditional sliding mode needs high-order derivative of feedback angle, it is difficult to implement traditional sliding mode in real hardware system. To solve these problems, a nonlinear differential and integral sliding mode control strategy is proposed. The integral term is introduced to reduce the influence of unmodeled disturbance and parameter perturbation. The stability analysis proves that the system state can track the desired target signal, and the tracking error e( t) tends to zero. In addition, in order to weaken the phenomenon of system chattering, this paper introduces a nonlinear differential control to increase the damping coefficient of the system. The simulation and experimental results show that the control law has good dynamic performance, high control accuracy, and strong anti-disturbance ability without chattering phenomenon. It is of great significance to improve the efficiency and safety of ship-borne manipulator operation, and this paper also provides useful reference for wave compensation system of other marine equipment.